Intellectual Evolution Method for Synthesis of Mobile Robot Control System

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Transcript of Intellectual Evolution Method for Synthesis of Mobile Robot Control System

Intellectual Evolution Method for Synthesis of Mobile Robot Control SystemAuthors:Diveev AskhatShmalko ElizavetaSofronova ElenaKhamadiyarov DamirSome historical factsNetwork OperatorThe numerical exampleGracias por su atenciónMichael O'Neill and Conor Ryan, 1999Ivan Zelinka, 2003John Koza, 1992Description of the objectAn example of the network operatorThe NetworkOperator MethodDifferential equations:Genetic ProgrammingMethod of Grammatical EvolutionMethod of Analytical ProgrammingNetwork Operator MethodAskhat Diveev, 2006Control Synthesis for a Mobile RobotControl constraints:Functionals:Terminal error:Time length:The set of initial values:Control system:Set of variables:Set of parametrs:Set of unary operations:Set of binary operations:The identity operation for unary operationsProperties of a Network operatorThe graph has no loops1st stepFinished2nd stepSparkLast stepStartAny non source node has at least one edge from a source nodeAny non sink node has at least one edge to a sink node[X][Q]Every source node corresponds to an element from the set of variables or the set of parametersOOEvery node corresponds to a binary operation from the set of binary operationsEvery edge corresponds to a unary operation from the set of unary operationsRules to calculate the mathematical expression by the network operatora) a unary operation is performed only for the edge that comes out from the node with no incoming edgesb) the edge is deleted from the graph once the unary operation is performedc) a binary operation in the node is performed right after the unary operation of the incoming edge is performedUnitelementd) the calculation is terminated when all edges are deleted from the graphX1X21100111112412An example of the network operatorX1X21100111112412X211001112412UnitelementX1X2110011112412Unitelement21NOM is based on anadjacency matrix of a directed graphX1X21100111112412123456The adjacency matrixAn example of the Network Operator Matrix (NOM)The Network Operator MatrixThe vector of nodes1. Initialize, generate a set of possible solutions

2. Evaluate each possible solution by performance functions

3. Select basic solutions in accordance with Pareto-rank

4. Distribute possible solutions on different bases inversely as Pareto-rank

6. Improve the set of possible solutions by replacing bad solutions with new good possible solutions

7. Form new basic solutions as the defined number of loops are repeated

8. Check the stopping criteria that are the defined number of loops are done or the best solution for the problem is foundThe Intellectual evolution methodThe set of network operators:Basic matrix:Null-variation:Set of vectors of variations:Part of parametrs in a Gray code:Network operator matrix:Vector of parametersNew Pareto-set with the solutions, that have zero Pareto-rankThe basic solutionwhereq1q2δ1211100001011111111111212634781116135The network operatorsThe network operator matrixThe network operator matrix of the obtained solutionThe obtained solution:whereCardinal of initial set of possible solutions: 512Number of generations: 128Number of crossovers in one generation: 256Number of generations between epochs: 32Number of basic solutions: 5Probability of mutation: 0.7The termination conditions are defined: Xf = 0, Yf = 0The mobile robot starts from the given initial conditionsThe robot starts from new initial conditions that differ from those used in synthesis processTrajectory of robot motion from point to pointSimulation with initial conditions x(0)=1, y(0)=1Simulation with initial conditions x(0)=-1, y(0)=1The unit element for binary operationsAdditional requirements for the program notationOnly unary operations or a digit 1 can be used as arguments of binary operations1O1[n]O2[m]O2[m][X][Q]QXiiorThose unary operations, that have the same parameters or variables as arguments cannot be arguments for binary operationsBinary operations or an element from the sets of variables and parameters can be used as arguments for unary operationsCybernetics and mechatronics departmentPeoples’ Friendship University of RussiaIEEECEC 20131